Questions tagged [schubert-cells]
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Intersection of certain subsets in a split connected reductive group $G$ related to affine open cover of $G/B$
Let $k$ be a field of characteristic zero and $G$ a split connected reductive group over $k$. Moreover, let $T$ be a split maximal torus of $G$ and $B\supset T$ a Borel subgroup. Additionally, we ...
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CW-structure on flag manifolds
I want to apologize in advance if my question is too elementary as I am not an expert in Lie theory. I have posted it before on stackexchange without receiving an answer.
Let $G$ be a compact Lie ...
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Trivial morphism between local cohomology groups
I have two questions concerning morphism between local cohomology groups which I think are related.
Let $G$ be a reductive group with Weyl group $W$ and $B \subset G$ a Borel. Let $X=G/B$ be the flag ...
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Union of Schubert cells being affine
Let $k$ be a field of characteristic zero, $G$ be a reductive group with a Borel $B$ and $\mathcal{F}:=G/B$ the associated flag variety. Let $W$ be the Weyl-group of G.
Then let $S \subset W$ and $Z=\...
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Generically intersecting Schubert cycles
I have a question about the the proof of Pieri's formula from Harris' and Eisenbuds's lecture "3264 and All That"on page 146. Before the proof we use this terminology (see page 139):
let $G=G(k,V)$...
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Flag variety over quaternions and its Hecke algebra
Consider cell decomposition of flag variety of $\mathbb{H}^{n}$ into orbits under the action of $B(\mathbb{H})$ - group of upper triangular matrices with coefficients in $\mathbb{H}$. I think cells ...
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Typo in a paper definition of Schubert cells?
In the paper "Quantum state transformations and the Schubert calculus" by Sumit Daftuar and Patrick Hayden (Annals of Physics 315 (2005) 80-122) on page 91, we have following notations:
$A_r$ denotes ...
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Can Schubert cells be defined, set theoretically, by less equations then the standard ones?
Let $V = \mathbb{C}^n$ with basis $e_1,\dots,e_n$, and $U = \langle e_1,\dots,e_k\rangle$. Let
$$\Sigma(U)=\{\sigma\in Gr(V,2)\mid \sigma\in U \}$$
be the Schubert cell of $2$-planes contained in $U$....
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Schubert calculus and Pieri's formula
In the lecture notes Grassmannians: the first example of a moduli space. MIT Open Course Ware. page 7:
Are there any formal publications (books/papers) where I can find the formula?
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Can Bruhat cells in semi simple groups be induced from matrices?
Let $G$ be a semisimple Lie group. Embed it as a subgroup into a special linear group of suitable rank, $SL(n)$ (real or complex). The question is: is it always possible to find such an embedding, ...
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Schubert problems to cycle class in Grassmanian
Say I have a family of linear spaces, and that I can solve all Schuber problems of that family (that is, how many members of the family pass through a set $S$ of linear spaces,
where we consider all ...
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Comparing the Kazhdan-Lusztig and Steinberg pre-orders
Both Kazhdan-Lusztig and Steinberg have defined pairs of preorders on $S_n$. Kazhdan and Lusztig's preorders come from their basis:
We write $x\leq_L y$ if any left ideal spanned by K-L basis ...
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Detailed proof of cup product equivalent to intersection
Consider a smooth, closed, compact finite-dim manifold. We have Poincare Duality to relate the cocycles and cycles.
I would like to know where I can find
a reference for a proof that the cup
...
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